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Energy of Particle in nx Level in 3D Box Formula

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Energy of Particle in Box along X axis is defined as the energy values that a particle can have residing in a level. Check FAQs

E x = \frac{{(n x)}^{2} \cdot {([hP])}^{2}}{8 \cdot m \cdot {(l x)}^{2}}

E_x - Energy of Particle in Box along X axis?n_x - Energy Levels along X axis?m - Mass of Particle?l_x - Length of Box along X axis?[hP] - Planck constant?

Energy of Particle in nx Level in 3D Box Example

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Here is how the Energy of Particle in nx Level in 3D Box equation looks like with Values.

Here is how the Energy of Particle in nx Level in 3D Box equation looks like with Units.

Here is how the Energy of Particle in nx Level in 3D Box equation looks like.

149.2403 = \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31 \cdot {(1.01)}^{2}}

149.2403eV = \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31kg \cdot {(1.01A)}^{2}}

149.2403 = \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31 \cdot {(1.01)}^{2}}

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Energy of Particle in nx Level in 3D Box Solution

Follow our step by step solution on how to calculate Energy of Particle in nx Level in 3D Box?

FIRST Step Consider the formula

E x = \frac{{(n x)}^{2} \cdot {([hP])}^{2}}{8 \cdot m \cdot {(l x)}^{2}}

Next Step Substitute values of Variables

∴

E x = \frac{{(2)}^{2} \cdot {([hP])}^{2}}{8 \cdot 9E-31kg \cdot {(1.01A)}^{2}}

Next Step Substitute values of Constants

∴

E x = \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31kg \cdot {(1.01A)}^{2}}

Next Step Convert Units

∴

E x = \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31kg \cdot {(1E-10m)}^{2}}

Next Step Prepare to Evaluate

∴

E x = \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31 \cdot {(1E-10)}^{2}}

Next Step Evaluate

∴

E x = 2.39109478237349E-17J

Next Step Convert to Output's Unit

∴

E x = 149.24033298945eV

LAST Step Rounding Answer

∴

E x = 149.2403eV

Energy of Particle in nx Level in 3D Box Formula Elements

Variables

Constants

Energy of Particle in Box along X axis

Energy of Particle in Box along X axis is defined as the energy values that a particle can have residing in a level.

Symbol: E_x

Measurement: EnergyUnit: eV

Note: Value can be positive or negative.

Formulas to find Energy of Particle in Box along X axis

Energy Levels along X axis

Energy Levels along X axis are the quantised levels where the particle may be present.

Symbol: n_x

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Energy Levels along X axis

Mass of Particle

Mass of Particle is defined as the energy of that system in a reference frame where it has zero momentum.

Symbol: m

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass of Particle

Length of Box along X axis

Length of Box along X axis gives us the dimension of the box in which the particle is kept.

Symbol: l_x

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Length of Box along X axis

Planck constant

Planck constant is a fundamental universal constant that defines the quantum nature of energy and relates the energy of a photon to its frequency.

Symbol: [hP]

Value: 6.626070040E-34

Other formulas in Particle in 3 Dimensional Box category

Go Energy of Particle in ny Level in 3D Box

E y = \frac{{(n y)}^{2} \cdot {([hP])}^{2}}{8 \cdot m \cdot {(l y)}^{2}}

Go Energy of Particle in nz Level in 3D Box

E z = \frac{{(n z)}^{2} \cdot {([hP])}^{2}}{8 \cdot m \cdot {(l z)}^{2}}

Go Total Energy of Particle in 3D Box

E = \frac{{(n x)}^{2} \cdot {([hP])}^{2}}{8 \cdot m \cdot {(l x)}^{2}} + \frac{{(n y)}^{2} \cdot {([hP])}^{2}}{8 \cdot m \cdot {(l y)}^{2}} + \frac{{(n z)}^{2} \cdot {([hP])}^{2}}{8 \cdot m \cdot {(l z)}^{2}}

Go Total Energy of Particle in Cubic Box

E = \frac{{([hP])}^{2} \cdot ({(n x)}^{2} + {(n y)}^{2} + {(n z)}^{2})}{8 \cdot m \cdot {(l)}^{2}}

How to Evaluate Energy of Particle in nx Level in 3D Box?

Energy of Particle in nx Level in 3D Box evaluator uses Energy of Particle in Box along X axis = ((Energy Levels along X axis)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along X axis)^2) to evaluate the Energy of Particle in Box along X axis, The Energy of Particle in nx Level in 3D Box formula is defined as the energy values that a particle can have residing in that level. Energy of Particle in Box along X axis is denoted by E_x symbol.

How to evaluate Energy of Particle in nx Level in 3D Box using this online evaluator? To use this online evaluator for Energy of Particle in nx Level in 3D Box, enter Energy Levels along X axis (n_x), Mass of Particle (m) & Length of Box along X axis (l_x) and hit the calculate button.

FAQs on Energy of Particle in nx Level in 3D Box

What is the formula to find Energy of Particle in nx Level in 3D Box?

The formula of Energy of Particle in nx Level in 3D Box is expressed as Energy of Particle in Box along X axis = ((Energy Levels along X axis)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along X axis)^2). Here is an example- 9.3E+20 = ((2)^2*([hP])^2)/(8*9E-31*(1.01E-10)^2).

How to calculate Energy of Particle in nx Level in 3D Box?

With Energy Levels along X axis (n_x), Mass of Particle (m) & Length of Box along X axis (l_x) we can find Energy of Particle in nx Level in 3D Box using the formula - Energy of Particle in Box along X axis = ((Energy Levels along X axis)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along X axis)^2). This formula also uses Planck constant .

Can the Energy of Particle in nx Level in 3D Box be negative?

Yes, the Energy of Particle in nx Level in 3D Box, measured in Energy can be negative.

Which unit is used to measure Energy of Particle in nx Level in 3D Box?

Energy of Particle in nx Level in 3D Box is usually measured using the Electron-Volt[eV] for Energy. Joule[eV], Kilojoule[eV], Gigajoule[eV] are the few other units in which Energy of Particle in nx Level in 3D Box can be measured.

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